In classical antiquity only round numbers — natural integers — were known, and mathematics was very different to the way it is today. But whereas the mathematics of this ancient era was in one sense more basic, it made use of many theoretical concepts and approaches that are no longer familiar to modern scientists. This chapter introduces three mathematical concepts or approaches that provided a foundation for classical Greek and Roman architecture. The first of these, which was equally significant for geometry and arithmetic, is concerned with the figurate representation of quantities. The second is associated with the visual comparison of magnitudes, and the last is the theory of mean proportions.